THE VOCABULARY
Instruments, concepts, and phenomena — the shared vocabulary of the site.
Gauge theory origins
The intellectual lineage from the 1865-1867 observation of gauge freedom in electromagnetism, through Hermann Weyl's 1918 unification attempt and 1929 retooling as a quantum-phase symmetry, to Yang-Mills 1954 and the Standard Model. The gauge principle is the template behind every fundamental force in nature.
Gauge transformation
A change A → A + ∇λ, V → V − ∂λ/∂t in the potentials that leaves all physical fields E and B unchanged. The freedom that defines what 'gauge' means.
Gaussian surface
An imaginary closed surface chosen to exploit symmetry when applying Gauss's law.
Generalised coordinates
Any set of independent variables that fully specifies a system's configuration. Not necessarily Cartesian.
Geodesic equation
d²x^μ/dλ² + Γ^μ_{αβ} (dx^α/dλ)(dx^β/dλ) = 0. The trajectory of a freely-falling particle in curved spacetime; the curve whose tangent is parallel-transported along itself. Generalises the Newtonian straight line. In GR, free-fall = geodesic motion.
GPS clock correction
The combined SR + GR clock-rate correction applied by every GPS satellite firmware: kinematic time dilation slows the orbiting clock by ~7 μs/day, gravitational time dilation speeds it up by ~45 μs/day, net correction ~+38 μs/day. Without the correction, position fixes would drift roughly 11 km per day.
Gradient
A vector that points in the direction of steepest increase of a scalar field, with magnitude equal to the rate of that increase.
gravitational field
The vector field g(r) = −GM/r² r̂ giving the acceleration any test mass would experience at each point in space.
Gravitational redshift
Photons climbing out of a gravitational potential lose energy and frequency: Δν/ν = gh/c² for a tower of height h on Earth's surface; equivalently, clocks at lower potential tick slower than clocks at higher potential. A direct consequence of the equivalence principle, derivable without the field equations.
gravity assist
Technique in which a spacecraft gains or loses speed by flying close to a planet, exchanging momentum through the planet's gravitational field.
Group velocity
The speed v_g = dω/dk at which a wave packet's envelope — and therefore its energy and information — propagates.
Group velocity (EM)
v_g = dω/dk. The speed at which a wave packet's envelope — and therefore its energy and information content — propagates. In a dispersive medium v_g differs from the phase velocity v_p = ω/k.
gyroscope
A rapidly spinning rotor on a gimbal or pivot, whose angular momentum resists reorientation — the workhorse of modern inertial navigation.
H-field
The auxiliary magnetic field H = B/μ₀ − M, in amperes per metre. Its circulation around a loop is determined by free currents only, ignoring bound currents inside magnetised matter.
Hamilton's equations
The first-order system q̇ = ∂H/∂p, ṗ = −∂H/∂q generating time evolution in phase space.
Hamiltonian
A scalar function H(q, p, t) whose partial derivatives, via Hamilton's equations, generate time evolution. For conservative systems, H = T + V.
Harmonic series
The ladder of integer-multiple frequencies that a bounded system supports above its fundamental.
Henry
The SI unit of inductance. One henry is the inductance of a coil in which a current changing at one ampere per second induces an EMF of one volt. Symbol: H. 1 H = 1 V·s/A.
Hertzian dipole
The idealised point-dipole antenna — an infinitesimally short conductor of length L ≪ λ carrying a uniform oscillating current I(t) = I₀ cos(ωt). Used as the basic radiating element from which the fields of all more complex antennas are built by superposition.
Hohmann transfer
The most fuel-efficient two-burn manoeuvre for moving between two circular orbits; uses a half-ellipse as the transfer path.
Holonomy
The rotation a vector picks up when parallel-transported around a closed loop on a manifold. Vanishes if and only if the curvature is zero. On a 2-sphere of radius R, transporting around a loop enclosing area A rotates the vector by A/R² — the spherical-triangle holonomy reveal that motivates the Riemann tensor.
Huygens's principle
Every point on a wavefront acts as a source of secondary spherical wavelets; the envelope of all the wavelets gives the wavefront at the next instant. Christiaan Huygens, 1678; generalised by Fresnel and Kirchhoff.
Hydrostatic
Relating to fluids at rest. In the hydrostatic limit, pressure varies only with depth: dp/dz = −ρg.
Hysteresis loop
The closed curve traced by B (or M) versus H in a ferromagnet under a cycled applied field. Its enclosed area equals the energy dissipated per unit volume per cycle.
Image charge
A fictitious charge placed outside the region of interest whose field, together with the real charge's field, satisfies the conductor's boundary conditions.
Impedance
Z = V/I for a component or network driven at a single frequency, generalising resistance to the complex plane. Z = R + jX, where R is the resistance (dissipative) and X is the reactance (energy-storing).
impulse
The change in momentum delivered by a force acting over a time interval: J = ∫F dt = Δp.
Incompressible flow
Fluid motion in which density is effectively constant. Liquids, and gases at Mach ≪ 1.
Induced charge
The surface charge that appears on a conductor in response to a nearby external charge, redistributed until the conductor's interior field is zero.
inelastic collision
A collision in which kinetic energy is not conserved; the missing energy goes into heat, sound, or deformation.